JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (4): 61-67.doi: 10.6040/j.issn.1671-9352.0.2016.521

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The judgement for the small compact perturbation of SVEP for upper triangular operator matrices

SONG Jia-jia1, CAO Xiao-hong1*, DAI Lei2   

  1. 1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China;
    2.College of Mathematics and Physics, Weinan Normal University, Weinan 714000, Shaanxi, China
  • Received:2016-12-30 Online:2017-04-20 Published:2017-04-11

Abstract: When A∈B(H), B∈B(K)are given, we denote by MC an upper triangular operator matrix, acting on the Hilbert space H⊕K, of the form MC=(A C0 B). The properties of the component A,B are discussed in the matrix such that MC satisfies the single-valued extension property of small compact perturbation by defining a kind of new resolvent set. The necessary and sufficient conditions for upper triangular operator matrix which satisfies the single-valued extension property under small compact perturbation are studied, and some examples are given to illustrate the essence of the conditions given in the main theorem.

Key words: the single-valued extension property, small compact perturbation, spectrum

CLC Number: 

  • O177.2
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